# ---
# title: 1499. Max Value of Equation
# id: problem1499
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Array, Sliding Window
# link: <https://leetcode.com/problems/max-value-of-equation/description/>
# hidden: true
# ---
# 
# Given an array `points` containing the coordinates of points on a 2D plane,
# sorted by the x-values, where `points[i] = [xi, yi]` such that `xi < xj` for
# all `1 <= i < j <= points.length`. You are also given an integer `k`.
# 
# Find the _maximum value of the equation_`yi + yj + |xi - xj|` where `|xi - xj|
# <= k` and `1 <= i < j <= points.length`. It is guaranteed that there exists at
# least one pair of points that satisfy the constraint `|xi - xj| <= k`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: points = [[1,3],[2,0],[5,10],[6,-10]], k = 1
#     Output: 4
#     Explanation: The first two points satisfy the condition |xi - xj| <= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.
#     No other pairs satisfy the condition, so we return the max of 4 and 1.
# 
# **Example 2:**
# 
#     
#     
#     Input: points = [[0,0],[3,0],[9,2]], k = 3
#     Output: 3
#     Explanation: Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.
#     
# 
# 
# 
# **Constraints:**
# 
#   * `2 <= points.length <= 10^5`
#   * `points[i].length == 2`
#   * `-10^8 <= points[i][0], points[i][1] <= 10^8`
#   * `0 <= k <= 2 * 10^8`
#   * `points[i][0] < points[j][0]` for all `1 <= i < j <= points.length`
#   * `xi` form a strictly increasing sequence.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
